Jegaraj, Terence Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces. (English) Zbl 1196.60055 Electron. Commun. Probab. 14, 552-559 (2009). Summary: We show that S. R. S. Varadhan’s [Commun. Pure Appl. Math. 20, 431–455 (1967; Zbl 1055.16503)] small time asymptotics for densities of the solution of a stochastic differential equation in \(R^{n}\) carries over to a Hilbert space-valued Ornstein-Uhlenbeck process whose transition semigroup is strongly Feller and symmetric. In the Hilbert space setting, densities are with respect to a Gaussian invariant measure. MSC: 60F99 Limit theorems in probability theory 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:small time asymptotics; densities; Hilbert space; Ornstein-Uhlenbeck Citations:Zbl 1055.16503 PDFBibTeX XMLCite \textit{T. Jegaraj}, Electron. Commun. Probab. 14, 552--559 (2009; Zbl 1196.60055) Full Text: DOI EuDML EMIS